<p><strong><em>Abstract</em></strong></p><p>Many observed phenomena, from the changing health of a patient to values on the<br/>stock market, are characterised by quantities that vary over time: stochastic processes<br/>are designed to study them. Much theoretical work has been done but virtually no<br/>modern books are available to show how the results can be applied. This book fills<br/>that gap by introducing practical methods of applying stochastic processes to an<br/>audience knowledgeable only in the basics of statistics. It covers almost all aspects<br/>of the subject and presents the theory in an easily accessible form that is highlighted<br/>by application to many examples. These examples arise from dozens of areas, from<br/>sociology through medicine to engineering. Complementing these are exercise sets<br/>making the book suited for introductory courses in stochastic processes.<br/>Software is provided within the freely available R system for the reader to be able<br/>to apply all the models presented.<br/></p><p><strong><em>Author</em></strong></p><p>J. K. LINDSEY is Professor of Quantitative Methodology, University of Li`ege. He<br/>is the author of 14 books and more than 120 scientific papers.</p><p> </p><p><strong><em><font size="5">Contents</font></em></strong></p>Preface page ix <p></p>Notation and symbols xiii <p></p><strong><em>Part I Basic principles 1</em></strong>
        <p></p>1 What is a stochastic process? 3 <p></p>1.1 Definition 3 <p></p>1.2 Dependence among states 10 <p></p>1.3 Selecting models 14 <p></p>2 Basics of statistical modelling 18 <p></p>2.1 Descriptive statistics 18 <p></p>2.2 Linear regression 21 <p></p>2.3 Categorical covariates 26 <p></p>2.4 Relaxing the assumptions 29 <p></p><strong><em>Part II Categorical state space 37</em></strong>
        <p></p>3 Survival processes 39 <p></p>3.1 Theory 39 <p></p>3.2 Right censoring 47 <p></p>3.3 Interval censoring 53 <p></p>3.4 Finite mixtures 57 <p></p>3.5 Models based directly on intensities 60 <p></p>3.6 Changing factors over a lifetime 64 <p></p>4 Recurrent events 71 <p></p>4.1 Theory 72 <p></p>4.2 Descriptive graphical techniques 83 <p></p>4.3 Counts of recurrent events 88 <p></p>4.4 Times between recurrent events 91 <p></p>5 Discrete-time Markov chains 101 <p></p>5.1 Theory 102 <p></p>5.2 Binary point processes 108 <p></p>5.3 Checking the assumptions 114 <p></p>5.4 Structured transition matrices 119 <p></p>  <p></p>6 Event histories 133 <p></p>6.1 Theory 133 <p></p>6.2 Models for missing observations 138 <p></p>6.3 Progressive states 142 <p></p>7 Dynamic models 151 <p></p>7.1 Serial dependence 152 <p></p>7.2 Hidden Markov models 161 <p></p>7.3 Overdispersed durations between recurrent events 167 <p></p>7.4 Overdispersed series of counts 178 <p></p>8 More complex dependencies 183 <p></p>8.1 Birth processes 183 <p></p>8.2 Autoregression 191 <p></p>8.3 Marked point processes 195 <p></p>8.4 Doubly stochastic processes 198 <p></p>8.5 Change points 202 <p></p><strong><em>Part III Continuous state space 211</em></strong>
        <p></p>9 Time series 213 <p></p>9.1 Descriptive graphical techniques 213 <p></p>9.2 Autoregression 216 <p></p>9.3 Spectral analysis 226 <p></p>10 Diffusion and volatility 233 <p></p>10.1 Wiener diffusion process 233 <p></p>10.2 Ornstein–Uhlenbeck diffusion process 238 <p></p>10.3 Heavy-tailed distributions 240 <p></p>10.4 ARCH models 249 <p></p>11 Dynamic models 255 <p></p>11.1 Kalman filtering and smoothing 255 <p></p>11.2 Hidden Markov models 259 <p></p>11.3 Overdispersed responses 262 <p></p>12 Growth curves 268 <p></p>12.1 Characteristics 268 <p></p>12.2 Exponential forms 269 <p></p>12.3 Sigmoidal curves 275 <p></p>12.4 Richards growth curve 278 <p></p>13 Compartment models 285 <p></p>13.1 Theory 285 <p></p>13.2 Modelling delays in elimination 289 <p></p>13.3 Measurements in two compartments 293 <p></p>14 Repeated measurements 303 <p></p>14.1 Random effects 303 <p></p>14.2 Normal random intercepts 306 <p></p>14.3 Normal random coefficients 310 <p></p>14.4 Gamma random effects 312 <p></p><p> </p>